create a 2D system in standard form that will produce all 0's in the last row of row ref

Question

this question is about a 2D system that needs three zeros in the bottom row of a matrix equation 

Answer 1

In ref form, any row with all zeros is a multiple of another row. In this case, since we need a 2D array, the bottom row must be a multiple of the first row. Here's an example of a 2D system that has a row of zeros in ref form

4x + 6y = 8

8x + 12y = 16

Turning the system in a matrix we get

4 6 8

8 12 16

And reducing it to ref form we get (divide the first row by 4 and subtract R2 by 8R1)

1 3/2 2

0 0 0